A177824 a(n) = (Fibonacci(n)*Fibonacci(n+7)) mod 7.

0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1, 0, 0, 6, 5, 1, 6, 2, 1

Offset

0,3

Comments

The function f(k,n) = (Fibonacci(n)*Fibonacci(n+k)) mod k appears to be periodic. The repeated values for successive values of k are

k=2...[0,0,1]

k=3...[0,2,1,0]

k=4...[0,1,0,2,3,2]

k=5...[3,3,2,2,0,2,2,3,3,0]

k=6...[0,1,3,2,3,1,0,5,3,4,3,5]

k=7...[0,0,6,5,1,6,2,1]

k=8...[0,2,7,2,0,5]

k=9...[0,1,8,0,6,4,2,6,3,7,5,3]

k=10..[0,9,4,6,1,0,6,1,4,4,5,4,4,1,6,0,1,6,4,9,0,4,9,6,6,5,6,6,9,4]

Periodicity of 8.

Links

Table of n, a(n) for n=0..95.

Maple

with(combinat):
seq((fibonacci(n)*fibonacci(n+7)) mod 7, n=0..50);

Mathematica

Table[Mod[Fibonacci[n]Fibonacci[n+7], 7], {n, 0, 100}] (* Harvey P. Dale, Oct 01 2017 *)

Crossrefs

Sequence in context: A320833 A216582 A340543 * A242000 A238181 A197517

Adjacent sequences: A177821 A177822 A177823 * A177825 A177826 A177827

Keyword

nonn

Author

Gary Detlefs, Dec 13 2010

Status

approved